{"paper":{"title":"On the geometry of four dimensional Riemannian manifold with a circulant metric and a circulant affinor structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Dimitar Razpopov","submitted_at":"2011-10-09T10:50:12Z","abstract_excerpt":"We consider a four dimensional Riemannian manifold M with a metric g and an affinor structure q. We note the local coordinates of g and q are circulant matrices. Their first orders are (A, B, C, B), A, B, C \\in FM and (0, 1, 0, 0), respectively.\n  Let \\nabla be the connection of g. Further, let mu_{1}, mu_{2},mu_{3}, mu_{4}, mu_{5}, mu_{6} be the sectional curvatures of 2-sections {x, qx}, {x, q^{2}x}, {q^{3}x, x}, {qx, q^{2}x}, {qx, q^{3}x}, {q^{2}x, q^{3}x} for arbitrary vector x in T_{p}M$, p is in M . Then we have that q^{4}=E; g(qx, qy)=g(x,y), x, y are in chiM.\n  The main results of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1820","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}